Abstract
Recall from Ch. 6 that a function u on T is in Lp(T) if and only if its Hubert transform Hu is. By virtue of (2.8) in Ch. 6, we can define the Hubert transform even for u ∈ L1(T) as a formal Fourier series; in general, it will not belong to L1(T) but merely be a distribution; cf. Remark 2.1 in Ch. 6. More precisely, Hu is in L1(T) if and only if u = Re f* for some f ∈ H1.
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© 1997 Springer-Verlag New York, Inc.
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Andersson, M. (1997). H1 and BMO. In: Topics in Complex Analysis. Universitex: Tracts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4042-6_10
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DOI: https://doi.org/10.1007/978-1-4612-4042-6_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94754-9
Online ISBN: 978-1-4612-4042-6
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